Ultimate Guide to First Year Maths (1 Viewer)

[Omium]

Ok I've decided to create an ultimate thread for First year Mathematics,

I'm hoping this will help future students in their first year maths

Studying in this Course

1) First year maths content is somewhat similar to 3unit Mathematics and 4unit Mathematics, However if you did 3unit math or 4 unit math do not become complacent as it is very hard to catch up if you fall behind. ( The 12 week semesters make it extremely hard to catch up)

2) Success in UNSW maths subjects is directly proportional to the amount of work you put in, There is NO possible way you will fail maths / get a low mark if you study hard, it really is that simple

3) Simply LOOK over the content before you go to a lecture so you have an idea of whats going on.

3) You need to put in hard work to suceed in this course as with any other course, you can't cram and expect to go well, Its very hard to derive mathematical equations as you simply "need to remember" the equations and so cramming will most likely confuse you when applying formulas

4) Maths can seem very boring (especially vectors) However this is necessary as it builds a strong foundation for further maths

Quiz's

1) Quiz's are basically free marks, They are very simple and sometimes are tutorial questions.

2) You have 3 attempts, record your answers down before you re-attempt.

3) For Questions which require definitions, Read over the tutorial notes.

4) Do the Quiz's with a friend, you will both get the same questions except sometimes with different values.

Maple

1) Someone from your class will have Maple on a USB, borrow it.

2) Initially you will find Maple difficult however it becomes much much easier and is a very powerful tool

3) There is usually a maple advisor in the maths labs who is always glad to help out.

4) Do ALL the practice questions, they are the HARDEST types of questions you will ever get, (They never come in the Maple exams as they are too difficult) However they become relatively simple after a while.


Good luck and Have fun.

Add any tips or comments if you find them helpful guys

(Forbidden would it be possible for you to POST some of your Maple answer Notes? )

 

[darkwolfzx]

i love u omium

PS I'll add linx to my sticky.

 

[Omium]

i love u omium

Ive decided to make a Guide for Physics and Maths, Lazarus is sticking them both
(He's already stickied physics)

I always wished someone told me this before i started both courses

 

[kevinx2]

repz 4 u

 

[sl123]

Cheers mate.

 

[lyounamu]

Very nice, mate. It will help me a lot for my future uni course decision. rep for you btw

 

[Forbidden.]

In my attached archive it should contain:

• Answers to MOST of the questions in the Practice Problems section of the information booklet of MATH1231 (2008 session 1)
• Answers to the Sample Maple Worksheet version A they give to students (which I believe is also in the information booklet)

I believe this should uncover the mysteries and doubts behind the underpinnings of many questions.
Salute to the comrades!

EDIT:

Remember, what sets Engineering apart from other degrees is it hardens you up a lot.
At UNSW Engineering you will be the elite of the elite.
I was faring fine in HSC 2-unit and struggling in 3-unit back then, but once you put the effort and some appreciation you will not fail. I assure you.

 

[Omium]

In my attached archive it should contain:

• Answers to MOST of the questions in the Practice Problems section of the information booklet of MATH1231 (2008 session 1)
• Answers to the Sample Maple Worksheet version A they give to students (which I believe is also in the information booklet)

I believe this should uncover the mysteries and doubts behind the underpinnings of many questions.
Salute to the comrades!

Awesome, Thanks forbidden

 

[lyounamu]

In my attached archive it should contain:

• Answers to MOST of the questions in the Practice Problems section of the information booklet of MATH1231 (2008 session 1)
• Answers to the Sample Maple Worksheet version A they give to students (which I believe is also in the information booklet)

I believe this should uncover the mysteries and doubts behind the underpinnings of many questions.
Salute to the comrades!

EDIT:

Remember, what sets Engineering apart from other degrees is it hardens you up a lot.
At UNSW Engineering you will be the elite of the elite.
I was faring fine in HSC 2-unit and struggling in 3-unit back then, but once you put the effort and some appreciation you will not fail. I assure you.

Thanks.

rep for you.

 

[sl123]

What did you guys use to open the MWS file extension?

 

[darkwolfzx]

maple program.

@Forbidden, I think you need to export the contents into a text file. Opening the mws worksheets in notepad produces garbage.

 

[Forbidden.]

Thanks.

rep for you.

Thank you kind sir.
Salute to the comrade.

What did you guys use to open the MWS file extension?

Why Maple of course!

maple program.

@Forbidden, I think you need to export the contents into a text file. Opening the mws worksheets in notepad produces garbage.

kinda ugly but here goes

***BEGIN CODE for Practice Problems Worksheet

Question 1
> restart;
> assume(k>1);
> limit(n^(-k),n=infinity);

0

Question 2
> restart;
> f:=x^2*y^2*exp(x^2+y^2);

2 2 2 2
f := x y exp(x + y )

> diff(f,y,x);

3 3 3 3
4 x y %1 + 4 x y %1 + 4 x y %1 + 4 x y %1

2 2
%1 := exp(x + y )

> factor(%);

2 2 2 2
4 x y exp(x + y ) (1 + y ) (x + 1)

Question 3
> restart;
> with(LinearAlgebra):
> interface(rtablesize=15):
> u := <seq(k^2, k=1..15)>;

[ 1]
[ ]
[ 4]
[ ]
[ 9]
[ ]
[ 16]
[ ]
[ 25]
[ ]
[ 36]
[ ]
[ 49]
[ ]
u := [ 64]
[ ]
[ 81]
[ ]
[100]
[ ]
[121]
[ ]
[144]
[ ]
[169]
[ ]
[196]
[ ]
[225]

> v := <seq(k^3, k=1..15)>;

[ 1]
[ ]
[ 8]
[ ]
[ 27]
[ ]
[ 64]
[ ]
[ 125]
[ ]
[ 216]
[ ]
[ 343]
[ ]
v := [ 512]
[ ]
[ 729]
[ ]
[1000]
[ ]
[1331]
[ ]
[1728]
[ ]
[2197]
[ ]
[2744]
[ ]
[3375]

> evalf(((u.v)/(v.v))*v, 3);

[0.0754]
[ ]
[0.603 ]
[ ]
[ 2.04 ]
[ ]
[ 4.83 ]
[ ]
[ 9.43 ]
[ ]
[ 16.3 ]
[ ]
[ 25.9 ]
[ ]
[ 38.6 ]
[ ]
[ 55.0 ]
[ ]
[ 75.4 ]
[ ]
[ 100. ]
[ ]
[ 130. ]
[ ]
[ 166. ]
[ ]
[ 207. ]
[ ]
[ 255. ]

Question 4
> restart;
> with(geom3d):
> point(A,[1,2,3])oint(B,[1,-3,5])oint(C,[0,2,4]):
> line(L1,[A,B]):
> line(L2,[C,[1,0,-2]]):
> plane(P1,[A,B,C]):
> plane(P2,[A,[3,0,-1]]):
Question 4 (a)
> evalf(convert(FindAngle(L1,L2),degrees),4);
>

70.58 degrees

Question 4 (b)
> distance(L1,L2);

1/2
5 129
--------
129

Question 4 (c)
> Equation(P1,[x,y,z]);

24 - 5 x - 2 y - 5 z = 0

Question 4 (d)
> Equation(L1,t);

[1, 2 - 5 t, 3 + 2 t]

Question 4 (e)
> NormalVector(P1);

[-5, -2, -5]

Question 4 (f)
> intersection(L3,P1,P2):
> evalf(FindAngle(L1,L3),4);

0.1312

Question 6
> restart;
> f:=(3*x^5+2*x^4+6*x^3+7*x^2+3*x-8)/(((x^2+1)^2)*(x^2-1));

5 4 3 2
3 x + 2 x + 6 x + 7 x + 3 x - 8
f := -----------------------------------
2 2 2
(x + 1) (x - 1)

> convert(f,parfrac,x);

7 11 13 13
---------- + --------- + --------- + -----------
2 8 (x + 1) 8 (x - 1) 2 2
4 (x + 1) 2 (x + 1)

> denom(op(3, %));

8 x - 8

>
>
Question 7 (a)
> restart;
> ODE:=(diff(y(x),x))-(x*y(x))-(x^3*y(x)^2)=0;

/d \ 3 2
ODE := |-- y(x)| - x y(x) - x y(x) = 0
\dx /

> dsolve({ODE,y(0)=1/3},y(x));

1
y(x) = --------------------
2
2 x
2 - x + exp(- ----)
2

Question 7 (b)
> rhs(%);

1
--------------------
2
2 x
2 - x + exp(- ----)
2

> simplify(subs(x=0,%));

1/3

Question 8
> restart;
> ODE:=((x^2)*(diff(y(x),x,x)))-(2*x*(diff(y(x),x)))+2*y(x)=x;
> dsolve({ODE,y(1)=0,D(y)(1)=0},y(x));

/ 2 \
2 |d | /d \
ODE := x |--- y(x)| - 2 x |-- y(x)| + 2 y(x) = x
| 2 | \dx /
\dx /


2
y(x) = x - x (ln(x) + 1)

Question 9
> restart;
> ODE:=(diff(y(x),x,x))+(k*y(x))=0;

/ 2 \
|d |
ODE := |--- y(x)| + k y(x) = 0
| 2 |
\dx /

> assume(k,negative);
> dsolve(ODE);

1/2 1/2
y(x) = _C1 exp((-k~) x) + _C2 exp(-(-k~) x)

Question 11
> restart;
> p:=sum((k+1)^2*x^k,k=0..20);

2 3 4 5 6 7 8
p := 1 + 4 x + 9 x + 16 x + 25 x + 36 x + 49 x + 64 x + 81 x

9 10 11 12 13 14
+ 100 x + 121 x + 144 x + 169 x + 196 x + 225 x

15 16 17 18 19 20
+ 256 x + 289 x + 324 x + 361 x + 400 x + 441 x

> q:=sum((k+1)^3*x^k,k=0..20);

2 3 4 5 6 7
q := 1 + 8 x + 27 x + 64 x + 125 x + 216 x + 343 x + 512 x

8 9 10 11 12
+ 729 x + 1000 x + 1331 x + 1728 x + 2197 x

13 14 15 16 17
+ 2744 x + 3375 x + 4096 x + 4913 x + 5832 x

18 19 20
+ 6859 x + 8000 x + 9261 x

> coeff(p*q, x^21);

2456124

Question 12
> restart;
> with(LinearAlgebra):
> f:=proc(u,v);
> ((u.v)/(v.v))*v
> end proc;

f := proc(u, v) (u . v)*v/v . v end proc

> u:=<1,2,3>;v:=<3,2,1>;

[1]
[ ]
u := [2]
[ ]
[3]


[3]
[ ]
v := [2]
[ ]
[1]

> f(u,v);

[15/7]
[ ]
[10/7]
[ ]
[5/7 ]

Question 13
> restart;
> f:=x-> arcsinh(cos(exp(x)));

f := x -> arcsinh(cos(exp(x)))

> D(f)(0);

sin(1)
- ----------------
2 1/2
(1 + cos(1) )

> evalf(%,10);

-0.7403212721

Question 14 a)
> restart;
> with(LinearAlgebra):
> A:=<<1,4,7>|<2,5,8>|<3,6,9>>;

[1 2 3]
[ ]
A := [4 5 6]
[ ]
[7 8 9]

> f:=proc(A)
> return ColumnDimension(A)-Rank(A);
> end proc;

f := proc(A)
return LinearAlgebra:-ColumnDimension(A)
- LinearAlgebra:-Rank(A)
end proc

> f(A);

1

Question 14 b)
> restart;
> with(LinearAlgebra):
> A:=<<1,5,9,13>|<2,6,10,14>|<3,7,11,15>|<4,8,12,16>>;

[ 1 2 3 4]
[ ]
[ 5 6 7 8]
A := [ ]
[ 9 10 11 12]
[ ]
[13 14 15 16]

> NullSpace(A);

[ 2] [ 1]
[ ] [ ]
[-3] [-2]
{[ ], [ ]}
[ 0] [ 1]
[ ] [ ]
[ 1] [ 0]

Question 20
> restart;
> for k from 1 to 10 do;
> sum(n^k,n=1..15):
> end do;
>

120


1240


14400


178312


2299200


30482920


412420800


5666482312


78800938560


1106532668200

Question 21
> restart;
> a[0]:=1:a[1]:=1:
> for k from 0 while evalf(a[k+1]) < 100 do;
> a[k+2]:=a[k+1]+a[k]:
> end do:
> a[k];

89

Question 22
> restart;
> a[0]:=0;a[1]:=exp(0);
> for n from 1 while evalf(abs(a[n]-a[n-1])) >= 10^(-5) do;
> a[n+1]:=evalf(exp(-a[n]));
> end do:
> a[n];

a[0] := 0


a[1] := 1


0.5671407814

Question 23
> restart;
> f:=proc(n);
> if n mod 3 = 0 then
> return (n^2)/9;
> else
> return (n^2-1)/3;
> end if;
> end proc;

f := proc(n)
if n mod 3 = 0 then return 1/9*n^2
else return 1/3*n^2 - 1/3
end if
end proc

> f(363);f(364);

14641


44165

>
>


***END CODE for Practice Problems Worksheet

EDIT:


***BEGIN CODE for Sample Version A

Question 1
> restart;
> p:=sum(n*x^n,n=1..12);

2 3 4 5 6 7 8 9
p := x + 2 x + 3 x + 4 x + 5 x + 6 x + 7 x + 8 x + 9 x

10 11 12
+ 10 x + 11 x + 12 x

> q:=product((n+x^2),n=1..6);

2 2 2 2 2 2
q := (1 + x ) (2 + x ) (3 + x ) (4 + x ) (5 + x ) (6 + x )

> p/q;
>

2 3 4 5 6 7 8 9 10
(x + 2 x + 3 x + 4 x + 5 x + 6 x + 7 x + 8 x + 9 x + 10 x

11 12 / 2 2 2 2
+ 11 x + 12 x ) / ((1 + x ) (2 + x ) (3 + x ) (4 + x )
/

2 2
(5 + x ) (6 + x ))

> numer(op(5,p/q));

1

Question 2
> restart;
> ODE:=diff(y(x),x)-x*y(x)+x*y(x)^2=0;

/d \ 2
ODE := |-- y(x)| - x y(x) + x y(x) = 0
\dx /

> dsolve({ODE,y(0)=1/2},y(x));

1
y(x) = ---------------
2
x
1 + exp(- ----)
2

> y:=rhs(%);

1
y := ---------------
2
x
1 + exp(- ----)
2

> dy:=diff(y,x);

2
x
x exp(- ----)
2
dy := ------------------
/ 2 \2
| x |
|1 + exp(- ----)|
\ 2 /

> evalf(subs(x=1,dy));

0.2350037121

Question 3
> restart;
> a[0]:=1:a[1]:=evalf(2+ln(1)):
> for n from 1 while evalf(abs(a[n]-a[n-1]))>=10^(-5) do:
> a[n+1]:=2+ln(a[n]):
> end do:
> a[n];

3.146191522

Question 4
> restart;
> with(geom3d):
> point(A,[1,2,3])oint(B,[-2,3,4])oint(C,[1,3,2]):
> line(L1,[A,B]):
> plane(P1,[C,[1,-2,1]]):
> plane(P2,x+y+z=1,[x,y,z]):
> intersection(L2,P1,P2):
> evalf(FindAngle(L1,L2),10);

0.5494672456

> distance(L1,L2);

1/2
17 6
-------
18

>

***END CODE for Sample Version A

Remember, these are code from the Maple worksheet exported as Plain Text!

 

[darkwolfzx]

Question 4
> restart;
> with(geom3d):
> point(A,[1,2,3])oint(B,[-2,3,4])oint(C,[1,3,2]):
> line(L1,[A,B]):
> plane(P1,[C,[1,-2,1]]):
> plane(P2,x+y+z=1,[x,y,z]):
> intersection(L2,P1,P2):
> evalf(FindAngle(L1,L2),10);

0.5494672456

> distance(L1,L2);

1/2
17 6
-------
18

>

***END CODE for Sample Version A

Remember, these are code from the Maple worksheet exported as Plain Text!

lol XD

 

[Forbidden.]

lol XD

I FUCKING LOL'D

OKAY FIX HEREEEE:

text:

>point(A,[1,2,3]):point(B,[-2,3,4]):point(C,[1,3,2]):

picture:

i put it in the same line to save space and paper if it were to be printed out.

yesireee

+rep to the UNSW comrade!

 

[Omium]

lol XD

loll
i knew something was up

 

[Omie Jay]

If possible, get into Milan Pahor's lectures and tutes.

Even if it means getting a 5 hr gap in ur timetable (looks at my monday timetable)

 

[darkwolfzx]

If possible, get into Milan Pahor's lectures and tutes.

Even if it means getting a 5 hr gap in ur timetable (looks at my monday timetable)

.

 

[Iruka]

Very good thread, this. We should have more like it.

Would you consider adding stuff about some of the second year courses that a lot of people do? I guess the problem is that all you engo guys go off and do your own variants of Linear Algebra and Several Variable Calculus.

 

[Omium]

Very good thread, this. We should have more like it.

Would you consider adding stuff about some of the second year courses that a lot of people do? I guess the problem is that all you engo guys go off and do your own variants of Linear Algebra and Several Variable Calculus.

Ideally im hoping a second year maths or physics student could post another thread like this one.

Or when i finish second year physics and second year engineering maths (MATH2019 and MATH2089) ill post up guides to them as well

 

[Forbidden.]

I noticed the current posters in this thread consists of engineers, a computer scientist and a mathematician.

Here's an incredibly brief rundown of the expected skills in each course

Offered in session 1 & 2

MATH1131 (Math 1A) - Do OK in HSC ext 1 OR blaze HSC 2-unit maths

MATH1141 (Higher Math 1A) - Own HSC ext 1 OR do very well in HSC ext 2.


Offered in session 2 & summer (OMG SUMMER!??!?!?!)

MATH1231 (Math 1B) - Typical 2nd session maths course, you have survived MATH1131 with just a conceded pass (grade of 45-49) or dropping down from higher maths?

MATH1241 (Higher Math1B) - g0t distinction in MATH1131? g0t credit in MATH1141? still love maths omg? this is for you.

note there are less lecture and tutorial class sizes for higher maths because you are all nerds (j/k, u guys are cool)

During enrolment check you have a:

• 2 hour lecture block (its half algebra half calculus)
• 1 hour tutorial class #1 (algebra or was it calculus?)
• 1 hour tutorial class #2 (calculus or was it algebra?)

you know who your lecturers names are but you wont know who your tutors will be until you attend the class for the first time.

Anyway,

http://ecx.images-amazon.com/images/I/511BRXTDXYL._SL500_AA240_.jpg

As of 2008, the above textbook is the 10th edition of Calculus One and Several Variables (authors are Sallas, Hille & Etgen) prescribed to students in MATH1131 (Maths 1A) and MATH1231 (Maths 1B) and the higher ones

You may hear lecturers insist you buy textbooks,
however, let's not forget there is something called a course pack (approx $55) consisting of information and notes for the above 1st year maths courses.
This is sufficient study material already, however if you believe you can shell out an extra $110 and have too much time on your hands you could buy the textbook.
Enough material is supplied through lectures and the course pack already!
But the textbook does cover calculus material not in the 1st year courses and often shows way of solving problems slightly different from lectures and the course packs.

you go to UNSW Bookshop and do a search and you find something like

Calculus One and Several Variables - Prescribed - $110
Course Pack - Prescribed - $55
??? - Recommended - $???
??? - Recommended - $???
??? - Recommended - $???

ignore all but the $55 if you are on a tight budget or you dont have too much time on your hands

But for the student in....

- Medical Science

They have a choice between MATH1131 (Maths 1A) or the less demanding MATH1031 (Maths for Life Sciences), well they could do physics as they need to juggle their electives around, many find they prefer MATH1131.
buy it for only one course for one semester and sell it off?
you be the judge.

- Computer Science

Higher Math/Math 1A and Higher Math/Math 1B is compulsory for computer science students

- Engineering (most majors)

lucky you, although the textbook Calculus One and Several Variables isnt prescribed for Engineering Maths (2nd year course), the big thousands-of-pages textbook will also cover content found in the course i.e. lasting you 3 semesters.


Discrete Maths - 1081

I ain't a Computer Science student myself but from other people it's not their type of course as I've heard:

Korean fob guy - "it ruins the beauty of maths"
Engineering Student Centre lady - "oh discrete maths has been hated for years"

So,
if this course is NOT compulsory (check the UNSW handbook for your program) as in you are not a Computer Science, Software Engineering , Electrical Engineering (for them its MATH1091 i think) student, avoid it.
Not only would you miss out on the suggested electives designated by your program authority you will be wasting your time!

Discrete Maths requires the same pre-reqs as MATH1131.